 Hey friends welcome back to this session on problem solving and today We are going to solve a problem related to number system and the question says represent minus 2 by 3 and 14 by 5 on a number line. Okay, so we have discussed this in detail in the concept lectures now time to problem Solve solve the problems. So how to do it? So this is how you have to do it, okay? So first of all draw a straight line in your answer scripts You should be using a scale and a or a ruler and a pencil to draw a number line and then Take a point as zero now depending upon what numbers are to be represented. You have to divide or graduate the number line into some Intervals or graduation. So let us say if you see the numbers are minus 2 by 3 and 14 by 5 It's not a big number. So hence I can afford to take big units here. So this is 1 2 3 Okay, and here it is the same thing 1 and 2. So now let me name it 1 2 and 3 Here it is negative 1 and minus 2. This is how you should first of all draw a number line Now if you see minus 2 by 3 clearly minus 2 by 3, where would it lie? It would it would lie between 0 and 1, isn't it because Minus 2 by 3 is definitely less than 0 because it's a negative number But since it's a fraction, it's not beyond 1. So minus 1 that is so hence it will be between 0 and 1 Isn't it now? So that means so that means how to find 2 by 3 between 0 and minus 1 minus 2 by 3 Sorry, so again the number is minus 2 by 3 So minus 2 by 3. What is the denominator guys? Denominator is 3. So you have to divide that interval in three parts. First of all, what is the step one step one is? This you know find out or identify which identify Identify what do you need to identify? the segment which you are going to the segment the segment where where the desired number Lies, okay. So where does this desired number lies which segment? So segment is between 0 and minus 1 How do I know it because 2 by 3 is definitely less than 0, but it is not more than my Less than 0, but it is definitely more than minus 1. So now next step is find the denominator find the Denominator right denominator. So in this case denominator is 3. So divide that segment into Divide the segment into divide the segment divide the segment into Number of parts number of parts Found in step 2 isn't it? So I in step 2 I found 3. So I'll divide in 3 equal parts, right? So 1 2 so 3 equal parts I divided 3 number of Equal parts number of equal parts found in 2 right now So hence minus 2 by 3 will be nothing, but this is 1 and this is 2. So this part is minus 2 by 3 This is how I represent minus 2 by 3. Similarly, the next is 14 upon 5 now What is 14 upon 5 guys 14 upon 5 can be written as 2 whole 4 upon 5 isn't it? So 2 whole 4 upon 5 now That means this number the segment to be identified is nothing but 2 and 3 because it is definitely more than 2 But less than 3. So it is lying between 2 and 3 Where in 2 and 3 so in the denominator here is 5. So I divide the denominator into 5 equal parts So I have to put 4 points 1 2 3 4. So this is not Properly divided. So I'll again so 4 parts are 5 parts are to divide. So 4 points. I would take 1 2 3 and 4 now if you see there 2 and 3 the segment between 2 and 3 Has been divided into 5 equal parts now 4 parts out of that. So starting from 2 so 1 2 3 and this one is the final Point right. So I usually you should encircle that and that becomes 14 upon 5 so hence this point here is 14 upon 5 this point here is minus 2 upon 3. This is how you'll Represent any fraction or a rational number on a number line